Of course reading is good for your English skills. The first is that you are adding to you lexicon (mental dictionary) every time you pick up a book. That alone will transfer to your writing. You will find your self applying the words you have read into you own writing.

The second is a little more difficult, there is a distinct difference between active and passive reading. Passive is when you are doing it for fun, and not necessarily retaining all the text has to offer. Active reading is a little more difficult to master. It is the process of absorbing all a text has to offer, this includes mechanics, style, voice, tone, etc. This is what I suggest you do in order to develop a better grasp on English. When reading a text, pay attention to the details (e.g. grammar and phrasing). By being an active reader you will begin storing and implementing those various nuances of the language into your writing.

English can be a difficult language at times, considering its quirky spelling and metaphors, but reading is a great way to familiarize yourself with it. Read all you can, it will always help, and never hinder.